Imported Upstream version 4.6.0.125

Former-commit-id: a2155e9bd80020e49e72e86c44da02a8ac0e57a4

mcs/class/referencesource/System.Numerics/System/Numerics/Complex.cs

@@ -0,0 +1,421 @@
+// ==++==
+// 
+//   Copyright (c) Microsoft Corporation.  All rights reserved.
+// 
+// ==--==
+/*=========================================================================
+**
+** Class: Complex
+**
+**
+** Purpose: 
+** This feature is intended to create Complex Number as a type 
+** that can be a part of the .NET framework (base class libraries).  
+** A complex number z is a number of the form z = x + yi, where x and y 
+** are real numbers, and i is the imaginary unit, with the property i2= -1.
+**
+**
+===========================================================================*/
+
+using System;
+using System.Globalization;
+using System.Diagnostics.CodeAnalysis;
+using System.Diagnostics.Contracts;
+
+namespace System.Numerics {
+
+#if !SILVERLIGHT
+    [Serializable]
+#endif // !SILVERLIGHT
+    public struct Complex : IEquatable<Complex>, IFormattable {
+
+        // --------------SECTION: Private Data members ----------- //
+
+        private Double m_real;
+        private Double m_imaginary;
+
+        // ---------------SECTION: Necessary Constants ----------- //
+
+        private const Double LOG_10_INV = 0.43429448190325;
+
+
+        // --------------SECTION: Public Properties -------------- //
+
+        public Double Real {
+            get {
+                return m_real;
+            }
+        }
+
+        public Double Imaginary {
+            get {
+                return m_imaginary;
+            }
+        }
+
+        public Double Magnitude {
+            get {
+                return Complex.Abs(this);
+            }
+        }
+
+        public Double Phase {
+            get {
+                return Math.Atan2(m_imaginary, m_real);
+            }
+        }
+
+        // --------------SECTION: Attributes -------------- //
+
+        public static readonly Complex Zero = new Complex(0.0, 0.0);
+        public static readonly Complex One = new Complex(1.0, 0.0);
+        public static readonly Complex ImaginaryOne = new Complex(0.0, 1.0);
+
+        // --------------SECTION: Constructors and factory methods -------------- //
+
+        public Complex(Double real, Double imaginary)  /* Constructor to create a complex number with rectangular co-ordinates  */
+        {
+            this.m_real = real;
+            this.m_imaginary = imaginary;
+        }
+
+        public static Complex FromPolarCoordinates(Double magnitude, Double phase) /* Factory method to take polar inputs and create a Complex object */
+        {
+            return new Complex((magnitude * Math.Cos(phase)), (magnitude * Math.Sin(phase)));
+        }
+
+        public static Complex Negate(Complex value) {
+            return -value;
+        }
+
+        public static Complex Add(Complex left, Complex right) {
+            return left + right;
+        }
+
+        public static Complex Subtract(Complex left, Complex right) {
+            return left - right;
+        }
+
+        public static Complex Multiply(Complex left, Complex right) {
+            return left * right;
+        }
+
+        public static Complex Divide(Complex dividend, Complex divisor) {
+            return dividend / divisor;
+        }
+
+        // --------------SECTION: Arithmetic Operator(unary) Overloading -------------- //
+        public static Complex operator -(Complex value)  /* Unary negation of a complex number */
+        {
+
+            return (new Complex((-value.m_real), (-value.m_imaginary)));
+        }
+
+        // --------------SECTION: Arithmetic Operator(binary) Overloading -------------- //       
+        public static Complex operator +(Complex left, Complex right) {
+            return (new Complex((left.m_real + right.m_real), (left.m_imaginary + right.m_imaginary)));
+
+        }
+
+        public static Complex operator -(Complex left, Complex right) {
+            return (new Complex((left.m_real - right.m_real), (left.m_imaginary - right.m_imaginary)));
+        }
+
+        public static Complex operator *(Complex left, Complex right) {
+            // Multiplication:  (a + bi)(c + di) = (ac -bd) + (bc + ad)i
+            Double result_Realpart = (left.m_real * right.m_real) - (left.m_imaginary * right.m_imaginary);
+            Double result_Imaginarypart = (left.m_imaginary * right.m_real) + (left.m_real * right.m_imaginary);
+            return (new Complex(result_Realpart, result_Imaginarypart));
+        }
+
+        public static Complex operator /(Complex left, Complex right) {
+            // Division : Smith's formula.
+            double a = left.m_real;
+            double b = left.m_imaginary;
+            double c = right.m_real;
+            double d = right.m_imaginary;
+
+            if (Math.Abs(d) < Math.Abs(c)) {
+                double doc = d / c;
+                return new Complex((a + b * doc) / (c + d * doc), (b - a * doc) / (c + d * doc));
+            } else {
+                double cod = c / d;
+                return new Complex((b + a * cod) / (d + c * cod), (-a + b * cod) / (d + c * cod));
+            }
+        }
+
+
+        // --------------SECTION: Other arithmetic operations  -------------- //
+
+        public static Double Abs(Complex value) {
+
+            if(Double.IsInfinity(value.m_real) || Double.IsInfinity(value.m_imaginary)) {
+                return double.PositiveInfinity;
+            }
+
+            // |value| == sqrt(a^2 + b^2)
+            // sqrt(a^2 + b^2) == a/a * sqrt(a^2 + b^2) = a * sqrt(a^2/a^2 + b^2/a^2)
+            // Using the above we can factor out the square of the larger component to dodge overflow.
+
+
+            double c = Math.Abs(value.m_real);
+            double d = Math.Abs(value.m_imaginary);
+
+            if (c > d) {
+                double r = d / c;
+                return c * Math.Sqrt(1.0 + r * r);
+            } else if (d == 0.0) {
+                return c;  // c is either 0.0 or NaN
+            } else {
+                double r = c / d;
+                return d * Math.Sqrt(1.0 + r * r);
+            }
+        }
+        public static Complex Conjugate(Complex value) {
+            // Conjugate of a Complex number: the conjugate of x+i*y is x-i*y 
+
+            return (new Complex(value.m_real, (-value.m_imaginary)));
+
+        }
+        public static Complex Reciprocal(Complex value) {
+            // Reciprocal of a Complex number : the reciprocal of x+i*y is 1/(x+i*y)
+            if ((value.m_real == 0) && (value.m_imaginary == 0)) {
+                return Complex.Zero;
+            }
+
+            return Complex.One / value;
+        }
+
+        // --------------SECTION: Comparison Operator(binary) Overloading -------------- //
+
+        public static bool operator ==(Complex left, Complex right) {
+            return ((left.m_real == right.m_real) && (left.m_imaginary == right.m_imaginary));
+
+
+        }
+        public static bool operator !=(Complex left, Complex right) {
+            return ((left.m_real != right.m_real) || (left.m_imaginary != right.m_imaginary));
+
+        }
+
+        // --------------SECTION: Comparison operations (methods implementing IEquatable<ComplexNumber>,IComparable<ComplexNumber>) -------------- //
+
+        public override bool Equals(object obj) {
+            if (!(obj is Complex)) return false;
+            return this == ((Complex)obj);
+        }
+        public bool Equals(Complex value) {
+            return ((this.m_real.Equals(value.m_real)) && (this.m_imaginary.Equals(value.m_imaginary)));
+
+        }
+
+        // --------------SECTION: Type-casting basic numeric data-types to ComplexNumber  -------------- //
+
+        public static implicit operator Complex(Int16 value) {
+            return (new Complex(value, 0.0));
+        }
+        public static implicit operator Complex(Int32 value) {
+            return (new Complex(value, 0.0));
+        }
+        public static implicit operator Complex(Int64 value) {
+            return (new Complex(value, 0.0));
+        }
+        [CLSCompliant(false)]
+        public static implicit operator Complex(UInt16 value) {
+            return (new Complex(value, 0.0));
+        }
+        [CLSCompliant(false)]
+        public static implicit operator Complex(UInt32 value) {
+            return (new Complex(value, 0.0));
+        }
+        [CLSCompliant(false)]
+        public static implicit operator Complex(UInt64 value) {
+            return (new Complex(value, 0.0));
+        }
+        [CLSCompliant(false)]
+        public static implicit operator Complex(SByte value) {
+            return (new Complex(value, 0.0));
+        }
+        public static implicit operator Complex(Byte value) {
+            return (new Complex(value, 0.0));
+        }
+        public static implicit operator Complex(Single value) {
+            return (new Complex(value, 0.0));
+        }
+        public static implicit operator Complex(Double value) {
+            return (new Complex(value, 0.0));
+        }
+        public static explicit operator Complex(BigInteger value) {
+            return (new Complex((Double)value, 0.0));
+        }
+        public static explicit operator Complex(Decimal value) {
+            return (new Complex((Double)value, 0.0));
+        }
+
+
+        // --------------SECTION: Formattig/Parsing options  -------------- //
+
+        public override String ToString() {
+            return (String.Format(CultureInfo.CurrentCulture, "({0}, {1})", this.m_real, this.m_imaginary));
+        }
+
+        public String ToString(String format) {
+            return (String.Format(CultureInfo.CurrentCulture, "({0}, {1})", this.m_real.ToString(format, CultureInfo.CurrentCulture), this.m_imaginary.ToString(format, CultureInfo.CurrentCulture)));
+        }
+
+        public String ToString(IFormatProvider provider) {
+            return (String.Format(provider, "({0}, {1})", this.m_real, this.m_imaginary));
+        }
+
+        public String ToString(String format, IFormatProvider provider) {
+            return (String.Format(provider, "({0}, {1})", this.m_real.ToString(format, provider), this.m_imaginary.ToString(format, provider)));
+        }
+
+
+        public override Int32 GetHashCode() {
+            Int32 n1 = 99999997;
+            Int32 hash_real = this.m_real.GetHashCode() % n1;
+            Int32 hash_imaginary = this.m_imaginary.GetHashCode();
+            Int32 final_hashcode = hash_real ^ hash_imaginary;
+            return (final_hashcode);
+        }
+
+
+
+        // --------------SECTION: Trigonometric operations (methods implementing ITrigonometric)  -------------- //
+
+        public static Complex Sin(Complex value) {
+            double a = value.m_real;
+            double b = value.m_imaginary;
+            return new Complex(Math.Sin(a) * Math.Cosh(b), Math.Cos(a) * Math.Sinh(b));
+        }
+
+        [SuppressMessage("Microsoft.Naming", "CA1704:IdentifiersShouldBeSpelledCorrectly", MessageId = "Sinh", Justification = "[....]: Existing Name")]
+        public static Complex Sinh(Complex value) /* Hyperbolic sin */
+        {
+            double a = value.m_real;
+            double b = value.m_imaginary;
+            return new Complex(Math.Sinh(a) * Math.Cos(b), Math.Cosh(a) * Math.Sin(b));
+
+        }
+        public static Complex Asin(Complex value) /* Arcsin */
+        {
+	    if ((value.m_imaginary == 0 && value.m_real < 0) || value.m_imaginary > 0)
+            {
+                return -Asin(-value);
+            }
+            return (-ImaginaryOne) * Log(ImaginaryOne * value + Sqrt(One - value * value));
+        }
+
+        public static Complex Cos(Complex value) {
+            double a = value.m_real;
+            double b = value.m_imaginary;
+            return new Complex(Math.Cos(a) * Math.Cosh(b), - (Math.Sin(a) * Math.Sinh(b)));
+        }
+
+        [SuppressMessage("Microsoft.Naming", "CA1704:IdentifiersShouldBeSpelledCorrectly", MessageId = "Cosh", Justification = "[....]: Existing Name")]
+        public static Complex Cosh(Complex value) /* Hyperbolic cos */
+        {
+            double a = value.m_real;
+            double b = value.m_imaginary;
+            return new Complex(Math.Cosh(a) * Math.Cos(b), Math.Sinh(a) * Math.Sin(b));
+        }
+        public static Complex Acos(Complex value) /* Arccos */
+        {
+            if ((value.m_imaginary == 0 && value.m_real > 0) || value.m_imaginary < 0)
+            {
+                return System.Math.PI - Acos(-value);
+            }
+            return (-ImaginaryOne) * Log(value + ImaginaryOne*Sqrt(One - (value * value)));
+
+        }
+        public static Complex Tan(Complex value) {
+            return (Sin(value) / Cos(value));
+        }
+
+        [SuppressMessage("Microsoft.Naming", "CA1704:IdentifiersShouldBeSpelledCorrectly", MessageId = "Tanh", Justification = "[....]: Existing Name")]
+        public static Complex Tanh(Complex value) /* Hyperbolic tan */
+        {
+            return (Sinh(value) / Cosh(value));
+        }
+        public static Complex Atan(Complex value) /* Arctan */
+        {
+            Complex Two = new Complex(2.0, 0.0);
+            return (ImaginaryOne / Two) * (Log(One - ImaginaryOne * value) - Log(One + ImaginaryOne * value));
+        }
+
+        // --------------SECTION: Other numerical functions  -------------- //        
+
+        public static Complex Log(Complex value) /* Log of the complex number value to the base of 'e' */
+        {
+            return (new Complex((Math.Log(Abs(value))), (Math.Atan2(value.m_imaginary, value.m_real))));
+
+        }
+        public static Complex Log(Complex value, Double baseValue) /* Log of the complex number to a the base of a double */
+        {
+            return (Log(value) / Log(baseValue));
+        }
+        public static Complex Log10(Complex value) /* Log to the base of 10 of the complex number */
+        {
+
+            Complex temp_log = Log(value);
+            return (Scale(temp_log, (Double)LOG_10_INV));
+
+        }
+        public static Complex Exp(Complex value) /* The complex number raised to e */
+        {
+            Double temp_factor = Math.Exp(value.m_real);
+            Double result_re = temp_factor * Math.Cos(value.m_imaginary);
+            Double result_im = temp_factor * Math.Sin(value.m_imaginary);
+            return (new Complex(result_re, result_im));
+        }
+
+        [SuppressMessage("Microsoft.Naming", "CA1704:IdentifiersShouldBeSpelledCorrectly", MessageId = "Sqrt", Justification = "[....]: Existing Name")]
+        public static Complex Sqrt(Complex value) /* Square root ot the complex number */
+        {
+            return Complex.FromPolarCoordinates(Math.Sqrt(value.Magnitude), value.Phase / 2.0);
+        }
+
+        public static Complex Pow(Complex value, Complex power) /* A complex number raised to another complex number */
+        {
+
+            if (power == Complex.Zero) {
+                return Complex.One;
+            }
+
+            if (value == Complex.Zero) {
+                return Complex.Zero;
+            }
+
+            double a = value.m_real;
+            double b = value.m_imaginary;
+            double c = power.m_real;
+            double d = power.m_imaginary;
+
+            double rho = Complex.Abs(value);
+            double theta = Math.Atan2(b, a);
+            double newRho = c * theta + d * Math.Log(rho);
+
+            double t = Math.Pow(rho, c) * Math.Pow(Math.E, -d * theta);
+
+            return new Complex(t * Math.Cos(newRho), t * Math.Sin(newRho));
+        }
+
+        public static Complex Pow(Complex value, Double power) // A complex number raised to a real number 
+        {
+            return Pow(value, new Complex(power, 0));
+        }
+
+
+
+        //--------------- SECTION: Private member functions for internal use -----------------------------------//
+
+        private static Complex Scale(Complex value, Double factor) {
+
+            Double result_re = factor * value.m_real;
+            Double result_im = factor * value.m_imaginary;
+            return (new Complex(result_re, result_im));
+        }
+
+    }
+}

mcs/class/referencesource/System.Numerics/System/Numerics/HashCodeHelper.cs

@@ -0,0 +1,16 @@
+// Copyright (c) Microsoft. All rights reserved.
+// Licensed under the MIT license. See LICENSE file in the project root for full license information.
+
+namespace System.Numerics
+{
+    internal static class HashCodeHelper
+    {
+        /// <summary>
+        /// Combines two hash codes, useful for combining hash codes of individual vector elements
+        /// </summary>
+        internal static int CombineHashCodes(int h1, int h2)
+        {
+            return (((h1 << 5) + h1) ^ h2);
+        }
+    }
+}

mcs/class/referencesource/System.Numerics/System/Numerics/JITIntrinsicAttribute.cs

@@ -0,0 +1,13 @@
+// Copyright (c) Microsoft. All rights reserved.
+// Licensed under the MIT license. See LICENSE file in the project root for full license information.
+
+namespace System.Numerics
+{
+    /// <summary>
+    /// An attribute that can be attached to JIT Intrinsic methods/properties
+    /// </summary>
+    [AttributeUsage(AttributeTargets.Method | AttributeTargets.Constructor | AttributeTargets.Property)]
+    internal class JitIntrinsicAttribute : Attribute
+    {
+    }
+}

mcs/class/referencesource/System.Numerics/System/Numerics/NumericsHelpers.cs

@@ -0,0 +1,360 @@
+// ==++==
+// 
+//   Copyright (c) Microsoft Corporation.  All rights reserved.
+// 
+// ==--==
+
+using System;
+using System.Diagnostics;
+using System.Diagnostics.Contracts;
+using System.Collections.Generic;
+using System.Runtime.InteropServices;
+using System.Text;
+
+namespace System.Numerics {
+
+    [StructLayout(LayoutKind.Explicit)]
+    internal struct DoubleUlong {
+      [FieldOffset(0)]
+      public double dbl;
+      [FieldOffset(0)]
+      public ulong uu;
+    }
+
+
+    internal static class NumericsHelpers {
+    private const int kcbitUint = 32;
+
+    public static void GetDoubleParts(double dbl, out int sign, out int exp, out ulong man, out bool fFinite) {
+      Contract.Ensures(Contract.ValueAtReturn(out sign) == +1 || Contract.ValueAtReturn(out sign) == -1);
+
+      DoubleUlong du;
+      du.uu = 0;
+      du.dbl = dbl;
+
+      sign = 1 - ((int)(du.uu >> 62) & 2);
+      man = du.uu & 0x000FFFFFFFFFFFFF;
+      exp = (int)(du.uu >> 52) & 0x7FF;
+      if (exp == 0) {
+        // Denormalized number.
+        fFinite = true;
+        if (man != 0)
+          exp = -1074;
+      }
+      else if (exp == 0x7FF) {
+        // NaN or Inifite.
+        fFinite = false;
+        exp = int.MaxValue;
+      }
+      else {
+        fFinite = true;
+        man |= 0x0010000000000000;
+        exp -= 1075;
+      }
+    }
+
+    public static double GetDoubleFromParts(int sign, int exp, ulong man) {
+      DoubleUlong du;
+      du.dbl = 0;
+
+      if (man == 0)
+        du.uu = 0;
+      else {
+        // Normalize so that 0x0010 0000 0000 0000 is the highest bit set.
+        int cbitShift = CbitHighZero(man) - 11;
+        if (cbitShift < 0)
+          man >>= -cbitShift;
+        else
+          man <<= cbitShift;
+        exp -= cbitShift;
+        Contract.Assert((man & 0xFFF0000000000000) == 0x0010000000000000);
+
+        // Move the point to just behind the leading 1: 0x001.0 0000 0000 0000
+        // (52 bits) and skew the exponent (by 0x3FF == 1023).
+        exp += 1075;
+
+        if (exp >= 0x7FF) {
+          // Infinity.
+          du.uu = 0x7FF0000000000000;
+        }
+        else if (exp <= 0) {
+          // Denormalized.
+          exp--;
+          if (exp < -52) {
+            // Underflow to zero.
+            du.uu = 0;
+          }
+          else {
+            du.uu = man >> -exp;
+            Contract.Assert(du.uu != 0);
+          }
+        }
+        else {
+          // Mask off the implicit high bit.
+          du.uu = (man & 0x000FFFFFFFFFFFFF) | ((ulong)exp << 52);
+        }
+      }
+
+      if (sign < 0)
+        du.uu |= 0x8000000000000000;
+
+      return du.dbl;
+    }
+
+
+
+    // Do an in-place twos complement of d and also return the result.
+    // "Dangerous" because it causes a mutation and needs to be used
+    // with care for immutable types
+    public static uint[] DangerousMakeTwosComplement(uint[] d) {
+        // first do complement and +1 as long as carry is needed
+        int i = 0;
+        uint v = 0;
+        for (; i < d.Length; i++) {
+            v = ~d[i] + 1;
+            d[i] = v;
+            if (v != 0) { i++; break; }
+        }
+        if (v != 0) {
+            // now ones complement is sufficient
+            for (; i < d.Length; i++) {
+                d[i] = ~d[i];
+            }
+        } else {
+            //??? this is weird
+            d = resize(d, d.Length + 1);
+            d[d.Length - 1] = 1;
+        }
+        return d;
+    }
+
+    public static uint[] resize(uint[] v, int len) {
+        if (v.Length == len) return v;
+        uint[] ret = new uint[len];
+        int n = System.Math.Min(v.Length, len);
+        for (int i = 0; i < n; i++) {
+            ret[i] = v[i];
+        }
+        return ret;
+    }
+
+    public static void Swap<T>(ref T a, ref T b) {
+      T tmp = a;
+      a = b;
+      b = tmp;
+    }
+
+    public static uint GCD(uint u1, uint u2) {
+      const int cvMax = 32;
+      if (u1 < u2)
+        goto LOther;
+    LTop:
+      Contract.Assert(u2 <= u1);
+      if (u2 == 0)
+        return u1;
+      for (int cv = cvMax; ; ) {
+        u1 -= u2;
+        if (u1 < u2)
+          break;
+        if (--cv == 0) {
+          u1 %= u2;
+          break;
+        }
+      }
+    LOther:
+      Contract.Assert(u1 < u2);
+      if (u1 == 0)
+        return u2;
+      for (int cv = cvMax; ; ) {
+        u2 -= u1;
+        if (u2 < u1)
+          break;
+        if (--cv == 0) {
+          u2 %= u1;
+          break;
+        }
+      }
+      goto LTop;
+    }
+
+    public static ulong GCD(ulong uu1, ulong uu2) {
+      const int cvMax = 32;
+      if (uu1 < uu2)
+        goto LOther;
+    LTop:
+      Contract.Assert(uu2 <= uu1);
+      if (uu1 <= uint.MaxValue)
+        goto LSmall;
+      if (uu2 == 0)
+        return uu1;
+      for (int cv = cvMax; ; ) {
+        uu1 -= uu2;
+        if (uu1 < uu2)
+          break;
+        if (--cv == 0) {
+          uu1 %= uu2;
+          break;
+        }
+      }
+    LOther:
+      Contract.Assert(uu1 < uu2);
+      if (uu2 <= uint.MaxValue)
+        goto LSmall;
+      if (uu1 == 0)
+        return uu2;
+      for (int cv = cvMax; ; ) {
+        uu2 -= uu1;
+        if (uu2 < uu1)
+          break;
+        if (--cv == 0) {
+          uu2 %= uu1;
+          break;
+        }
+      }
+      goto LTop;
+
+    LSmall:
+      uint u1 = (uint)uu1;
+      uint u2 = (uint)uu2;
+      if (u1 < u2)
+        goto LOtherSmall;
+    LTopSmall:
+      Contract.Assert(u2 <= u1);
+      if (u2 == 0)
+        return u1;
+      for (int cv = cvMax; ; ) {
+        u1 -= u2;
+        if (u1 < u2)
+          break;
+        if (--cv == 0) {
+          u1 %= u2;
+          break;
+        }
+      }
+    LOtherSmall:
+      Contract.Assert(u1 < u2);
+      if (u1 == 0)
+        return u2;
+      for (int cv = cvMax; ; ) {
+        u2 -= u1;
+        if (u2 < u1)
+          break;
+        if (--cv == 0) {
+          u2 %= u1;
+          break;
+        }
+      }
+      goto LTopSmall;
+    }
+
+    public static ulong MakeUlong(uint uHi, uint uLo) {
+      return ((ulong)uHi << kcbitUint) | uLo;
+    }
+
+    public static uint GetLo(ulong uu) {
+      return (uint)uu;
+    }
+
+    public static uint GetHi(ulong uu) {
+      return (uint)(uu >> kcbitUint);
+    }
+
+    public static uint Abs(int a) {
+      uint mask = (uint)(a >> 31);
+      return ((uint)a ^ mask) - mask;
+    }
+
+//    public static ulong Abs(long a) {
+//      ulong mask = (ulong)(a >> 63);
+//      return ((ulong)a ^ mask) - mask;
+//    }
+
+    public static uint CombineHash(uint u1, uint u2) {
+      return ((u1 << 7) | (u1 >> 25)) ^ u2;
+    }
+
+    public static int CombineHash(int n1, int n2) {
+      return (int)CombineHash((uint)n1, (uint)n2);
+    }
+    public static int CbitHighZero(uint u) {
+      if (u == 0)
+        return 32;
+
+      int cbit = 0;
+      if ((u & 0xFFFF0000) == 0) {
+        cbit += 16;
+        u <<= 16;
+      }
+      if ((u & 0xFF000000) == 0) {
+        cbit += 8;
+        u <<= 8;
+      }
+      if ((u & 0xF0000000) == 0) {
+        cbit += 4;
+        u <<= 4;
+      }
+      if ((u & 0xC0000000) == 0) {
+        cbit += 2;
+        u <<= 2;
+      }
+      if ((u & 0x80000000) == 0)
+        cbit += 1;
+      return cbit;
+    }
+
+    public static int CbitLowZero(uint u) {
+      if (u == 0)
+        return 32;
+
+      int cbit = 0;
+      if ((u & 0x0000FFFF) == 0) {
+        cbit += 16;
+        u >>= 16;
+      }
+      if ((u & 0x000000FF) == 0) {
+        cbit += 8;
+        u >>= 8;
+      }
+      if ((u & 0x0000000F) == 0) {
+        cbit += 4;
+        u >>= 4;
+      }
+      if ((u & 0x00000003) == 0) {
+        cbit += 2;
+        u >>= 2;
+      }
+      if ((u & 0x00000001) == 0)
+        cbit += 1;
+      return cbit;
+    }
+
+    public static int CbitHighZero(ulong uu) {
+      if ((uu & 0xFFFFFFFF00000000) == 0)
+        return 32 + CbitHighZero((uint)uu);
+      return CbitHighZero((uint)(uu >> 32));
+    }
+
+//    public static int CbitLowZero(ulong uu) {
+//      if ((uint)uu == 0)
+//        return 32 + CbitLowZero((uint)(uu >> 32));
+//      return CbitLowZero((uint)uu);
+//    }
+//
+//    public static int Cbit(uint u) {
+//      u = (u & 0x55555555) + ((u >> 1) & 0x55555555);
+//      u = (u & 0x33333333) + ((u >> 2) & 0x33333333);
+//      u = (u & 0x0F0F0F0F) + ((u >> 4) & 0x0F0F0F0F);
+//      u = (u & 0x00FF00FF) + ((u >> 8) & 0x00FF00FF);
+//      return (int)((ushort)u + (ushort)(u >> 16));
+//    }
+//
+//    static int Cbit(ulong uu) {
+//      uu = (uu & 0x5555555555555555) + ((uu >> 1) & 0x5555555555555555);
+//      uu = (uu & 0x3333333333333333) + ((uu >> 2) & 0x3333333333333333);
+//      uu = (uu & 0x0F0F0F0F0F0F0F0F) + ((uu >> 4) & 0x0F0F0F0F0F0F0F0F);
+//      uu = (uu & 0x00FF00FF00FF00FF) + ((uu >> 8) & 0x00FF00FF00FF00FF);
+//      uu = (uu & 0x0000FFFF0000FFFF) + ((uu >> 16) & 0x0000FFFF0000FFFF);
+//      return (int)((uint)uu + (uint)(uu >> 32));
+//    }
+  }
+}

mcs/class/referencesource/System.Numerics/System/Numerics/Plane.cs

@@ -0,0 +1,366 @@
+// Copyright (c) Microsoft. All rights reserved.
+// Licensed under the MIT license. See LICENSE file in the project root for full license information.
+
+using System.Globalization;
+using System.Runtime.CompilerServices;
+
+namespace System.Numerics
+{
+    /// <summary>
+    /// A structure encapsulating a 3D Plane
+    /// </summary>
+    public struct Plane : IEquatable<Plane>
+    {
+        /// <summary>
+        /// The normal vector of the Plane.
+        /// </summary>
+        public Vector3 Normal;
+        /// <summary>
+        /// The distance of the Plane along its normal from the origin.
+        /// </summary>
+        public float D;
+
+        /// <summary>
+        /// Constructs a Plane from the X, Y, and Z components of its normal, and its distance from the origin on that normal.
+        /// </summary>
+        /// <param name="x">The X-component of the normal.</param>
+        /// <param name="y">The Y-component of the normal.</param>
+        /// <param name="z">The Z-component of the normal.</param>
+        /// <param name="d">The distance of the Plane along its normal from the origin.</param>
+        public Plane(float x, float y, float z, float d)
+        {
+            Normal = new Vector3(x, y, z);
+            this.D = d;
+        }
+
+        /// <summary>
+        /// Constructs a Plane from the given normal and distance along the normal from the origin.
+        /// </summary>
+        /// <param name="normal">The Plane's normal vector.</param>
+        /// <param name="d">The Plane's distance from the origin along its normal vector.</param>
+        public Plane(Vector3 normal, float d)
+        {
+            this.Normal = normal;
+            this.D = d;
+        }
+
+        /// <summary>
+        /// Constructs a Plane from the given Vector4.
+        /// </summary>
+        /// <param name="value">A vector whose first 3 elements describe the normal vector, 
+        /// and whose W component defines the distance along that normal from the origin.</param>
+        public Plane(Vector4 value)
+        {
+            Normal = new Vector3(value.X, value.Y, value.Z);
+            D = value.W;
+        }
+
+        /// <summary>
+        /// Creates a Plane that contains the three given points.
+        /// </summary>
+        /// <param name="point1">The first point defining the Plane.</param>
+        /// <param name="point2">The second point defining the Plane.</param>
+        /// <param name="point3">The third point defining the Plane.</param>
+        /// <returns>The Plane containing the three points.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Plane CreateFromVertices(Vector3 point1, Vector3 point2, Vector3 point3)
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                Vector3 a = point2 - point1;
+                Vector3 b = point3 - point1;
+
+                // N = Cross(a, b)
+                Vector3 n = Vector3.Cross(a, b);
+                Vector3 normal = Vector3.Normalize(n);
+
+                // D = - Dot(N, point1)
+                float d = -Vector3.Dot(normal, point1);
+
+                return new Plane(normal, d);
+            }
+            else
+            {
+                float ax = point2.X - point1.X;
+                float ay = point2.Y - point1.Y;
+                float az = point2.Z - point1.Z;
+
+                float bx = point3.X - point1.X;
+                float by = point3.Y - point1.Y;
+                float bz = point3.Z - point1.Z;
+
+                // N=Cross(a,b)
+                float nx = ay * bz - az * by;
+                float ny = az * bx - ax * bz;
+                float nz = ax * by - ay * bx;
+
+                // Normalize(N)
+                float ls = nx * nx + ny * ny + nz * nz;
+                float invNorm = 1.0f / (float)Math.Sqrt((double)ls);
+
+                Vector3 normal = new Vector3(
+                    nx * invNorm,
+                    ny * invNorm,
+                    nz * invNorm);
+
+                return new Plane(
+                    normal,
+                    -(normal.X * point1.X + normal.Y * point1.Y + normal.Z * point1.Z));
+            }
+        }
+
+        /// <summary>
+        /// Creates a new Plane whose normal vector is the source Plane's normal vector normalized.
+        /// </summary>
+        /// <param name="value">The source Plane.</param>
+        /// <returns>The normalized Plane.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Plane Normalize(Plane value)
+        {
+            const float FLT_EPSILON = 1.192092896e-07f; // smallest such that 1.0+FLT_EPSILON != 1.0
+            if (Vector.IsHardwareAccelerated)
+            {
+                float normalLengthSquared = value.Normal.LengthSquared();
+                if (Math.Abs(normalLengthSquared - 1.0f) < FLT_EPSILON)
+                {
+                    // It already normalized, so we don't need to farther process.
+                    return value;
+                }
+                float normalLength = (float)Math.Sqrt(normalLengthSquared);
+                return new Plane(
+                    value.Normal / normalLength,
+                    value.D / normalLength);
+            }
+            else
+            {
+                float f = value.Normal.X * value.Normal.X + value.Normal.Y * value.Normal.Y + value.Normal.Z * value.Normal.Z;
+
+                if (Math.Abs(f - 1.0f) < FLT_EPSILON)
+                {
+                    return value; // It already normalized, so we don't need to further process.
+                }
+
+                float fInv = 1.0f / (float)Math.Sqrt(f);
+
+                return new Plane(
+                    value.Normal.X * fInv,
+                    value.Normal.Y * fInv,
+                    value.Normal.Z * fInv,
+                    value.D * fInv);
+            }
+        }
+
+        /// <summary>
+        /// Transforms a normalized Plane by a Matrix.
+        /// </summary>
+        /// <param name="plane"> The normalized Plane to transform. 
+        /// This Plane must already be normalized, so that its Normal vector is of unit length, before this method is called.</param>
+        /// <param name="matrix">The transformation matrix to apply to the Plane.</param>
+        /// <returns>The transformed Plane.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Plane Transform(Plane plane, Matrix4x4 matrix)
+        {
+            Matrix4x4 m;
+            Matrix4x4.Invert(matrix, out m);
+
+            float x = plane.Normal.X, y = plane.Normal.Y, z = plane.Normal.Z, w = plane.D;
+
+            return new Plane(
+                x * m.M11 + y * m.M12 + z * m.M13 + w * m.M14,
+                x * m.M21 + y * m.M22 + z * m.M23 + w * m.M24,
+                x * m.M31 + y * m.M32 + z * m.M33 + w * m.M34,
+                x * m.M41 + y * m.M42 + z * m.M43 + w * m.M44);
+        }
+
+        /// <summary>
+        ///  Transforms a normalized Plane by a Quaternion rotation.
+        /// </summary>
+        /// <param name="plane"> The normalized Plane to transform.
+        /// This Plane must already be normalized, so that its Normal vector is of unit length, before this method is called.</param>
+        /// <param name="rotation">The Quaternion rotation to apply to the Plane.</param>
+        /// <returns>A new Plane that results from applying the rotation.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Plane Transform(Plane plane, Quaternion rotation)
+        {
+            // Compute rotation matrix.
+            float x2 = rotation.X + rotation.X;
+            float y2 = rotation.Y + rotation.Y;
+            float z2 = rotation.Z + rotation.Z;
+
+            float wx2 = rotation.W * x2;
+            float wy2 = rotation.W * y2;
+            float wz2 = rotation.W * z2;
+            float xx2 = rotation.X * x2;
+            float xy2 = rotation.X * y2;
+            float xz2 = rotation.X * z2;
+            float yy2 = rotation.Y * y2;
+            float yz2 = rotation.Y * z2;
+            float zz2 = rotation.Z * z2;
+
+            float m11 = 1.0f - yy2 - zz2;
+            float m21 = xy2 - wz2;
+            float m31 = xz2 + wy2;
+
+            float m12 = xy2 + wz2;
+            float m22 = 1.0f - xx2 - zz2;
+            float m32 = yz2 - wx2;
+
+            float m13 = xz2 - wy2;
+            float m23 = yz2 + wx2;
+            float m33 = 1.0f - xx2 - yy2;
+
+            float x = plane.Normal.X, y = plane.Normal.Y, z = plane.Normal.Z;
+
+            return new Plane(
+                x * m11 + y * m21 + z * m31,
+                x * m12 + y * m22 + z * m32,
+                x * m13 + y * m23 + z * m33,
+                plane.D);
+        }
+
+        /// <summary>
+        /// Calculates the dot product of a Plane and Vector4.
+        /// </summary>
+        /// <param name="plane">The Plane.</param>
+        /// <param name="value">The Vector4.</param>
+        /// <returns>The dot product.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static float Dot(Plane plane, Vector4 value)
+        {
+            return plane.Normal.X * value.X +
+                   plane.Normal.Y * value.Y +
+                   plane.Normal.Z * value.Z +
+                   plane.D * value.W;
+        }
+
+        /// <summary>
+        /// Returns the dot product of a specified Vector3 and the normal vector of this Plane plus the distance (D) value of the Plane.
+        /// </summary>
+        /// <param name="plane">The plane.</param>
+        /// <param name="value">The Vector3.</param>
+        /// <returns>The resulting value.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static float DotCoordinate(Plane plane, Vector3 value)
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                return Vector3.Dot(plane.Normal, value) + plane.D;
+            }
+            else
+            {
+                return plane.Normal.X * value.X +
+                       plane.Normal.Y * value.Y +
+                       plane.Normal.Z * value.Z +
+                       plane.D;
+            }
+        }
+
+        /// <summary>
+        /// Returns the dot product of a specified Vector3 and the Normal vector of this Plane.
+        /// </summary>
+        /// <param name="plane">The plane.</param>
+        /// <param name="value">The Vector3.</param>
+        /// <returns>The resulting dot product.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static float DotNormal(Plane plane, Vector3 value)
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                return Vector3.Dot(plane.Normal, value);
+            }
+            else
+            {
+                return plane.Normal.X * value.X +
+                       plane.Normal.Y * value.Y +
+                       plane.Normal.Z * value.Z;
+            }
+        }
+
+        /// <summary>
+        /// Returns a boolean indicating whether the two given Planes are equal.
+        /// </summary>
+        /// <param name="value1">The first Plane to compare.</param>
+        /// <param name="value2">The second Plane to compare.</param>
+        /// <returns>True if the Planes are equal; False otherwise.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static bool operator ==(Plane value1, Plane value2)
+        {
+            return (value1.Normal.X == value2.Normal.X &&
+                    value1.Normal.Y == value2.Normal.Y &&
+                    value1.Normal.Z == value2.Normal.Z &&
+                    value1.D == value2.D);
+        }
+
+        /// <summary>
+        /// Returns a boolean indicating whether the two given Planes are not equal.
+        /// </summary>
+        /// <param name="value1">The first Plane to compare.</param>
+        /// <param name="value2">The second Plane to compare.</param>
+        /// <returns>True if the Planes are not equal; False if they are equal.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static bool operator !=(Plane value1, Plane value2)
+        {
+            return (value1.Normal.X != value2.Normal.X ||
+                    value1.Normal.Y != value2.Normal.Y ||
+                    value1.Normal.Z != value2.Normal.Z ||
+                    value1.D != value2.D);
+        }
+
+        /// <summary>
+        /// Returns a boolean indicating whether the given Plane is equal to this Plane instance.
+        /// </summary>
+        /// <param name="other">The Plane to compare this instance to.</param>
+        /// <returns>True if the other Plane is equal to this instance; False otherwise.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public bool Equals(Plane other)
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                return this.Normal.Equals(other.Normal) && this.D == other.D;
+            }
+            else
+            {
+                return (Normal.X == other.Normal.X &&
+                        Normal.Y == other.Normal.Y &&
+                        Normal.Z == other.Normal.Z &&
+                        D == other.D);
+            }
+        }
+
+        /// <summary>
+        /// Returns a boolean indicating whether the given Object is equal to this Plane instance.
+        /// </summary>
+        /// <param name="obj">The Object to compare against.</param>
+        /// <returns>True if the Object is equal to this Plane; False otherwise.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public override bool Equals(object obj)
+        {
+            if (obj is Plane)
+            {
+                return Equals((Plane)obj);
+            }
+
+            return false;
+        }
+
+        /// <summary>
+        /// Returns a String representing this Plane instance.
+        /// </summary>
+        /// <returns>The string representation.</returns>
+        public override string ToString()
+        {
+            CultureInfo ci = CultureInfo.CurrentCulture;
+
+            return String.Format(ci, "{{Normal:{0} D:{1}}}", Normal.ToString(), D.ToString(ci));
+        }
+
+        /// <summary>
+        /// Returns the hash code for this instance.
+        /// </summary>
+        /// <returns>The hash code.</returns>
+        public override int GetHashCode()
+        {
+            return Normal.GetHashCode() + D.GetHashCode();
+        }
+    }
+}

mcs/class/referencesource/System.Numerics/System/Numerics/Vector2.cs

@@ -0,0 +1,451 @@
+// Copyright (c) Microsoft. All rights reserved.
+// Licensed under the MIT license. See LICENSE file in the project root for full license information.
+
+using System.Globalization;
+using System.Runtime.CompilerServices;
+using System.Text;
+
+namespace System.Numerics
+{
+    /// <summary>
+    /// A structure encapsulating two single precision floating point values and provides hardware accelerated methods.
+    /// </summary>
+    public partial struct Vector2 : IEquatable<Vector2>, IFormattable
+    {
+        #region Public Static Properties
+        /// <summary>
+        /// Returns the vector (0,0).
+        /// </summary>
+        public static Vector2 Zero { get { return new Vector2(); } }
+        /// <summary>
+        /// Returns the vector (1,1).
+        /// </summary>
+        public static Vector2 One { get { return new Vector2(1.0f, 1.0f); } }
+        /// <summary>
+        /// Returns the vector (1,0).
+        /// </summary>
+        public static Vector2 UnitX { get { return new Vector2(1.0f, 0.0f); } }
+        /// <summary>
+        /// Returns the vector (0,1).
+        /// </summary>
+        public static Vector2 UnitY { get { return new Vector2(0.0f, 1.0f); } }
+        #endregion Public Static Properties
+
+        #region Public instance methods
+        /// <summary>
+        /// Returns the hash code for this instance.
+        /// </summary>
+        /// <returns>The hash code.</returns>
+        public override int GetHashCode()
+        {
+            int hash = this.X.GetHashCode();
+            hash = HashCodeHelper.CombineHashCodes(hash, this.Y.GetHashCode());
+            return hash;
+        }
+
+        /// <summary>
+        /// Returns a boolean indicating whether the given Object is equal to this Vector2 instance.
+        /// </summary>
+        /// <param name="obj">The Object to compare against.</param>
+        /// <returns>True if the Object is equal to this Vector2; False otherwise.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public override bool Equals(object obj)
+        {
+            if (!(obj is Vector2))
+                return false;
+            return Equals((Vector2)obj);
+        }
+
+        /// <summary>
+        /// Returns a String representing this Vector2 instance.
+        /// </summary>
+        /// <returns>The string representation.</returns>
+        public override string ToString()
+        {
+            return ToString("G", CultureInfo.CurrentCulture);
+        }
+
+        /// <summary>
+        /// Returns a String representing this Vector2 instance, using the specified format to format individual elements.
+        /// </summary>
+        /// <param name="format">The format of individual elements.</param>
+        /// <returns>The string representation.</returns>
+        public string ToString(string format)
+        {
+            return ToString(format, CultureInfo.CurrentCulture);
+        }
+
+        /// <summary>
+        /// Returns a String representing this Vector2 instance, using the specified format to format individual elements 
+        /// and the given IFormatProvider.
+        /// </summary>
+        /// <param name="format">The format of individual elements.</param>
+        /// <param name="formatProvider">The format provider to use when formatting elements.</param>
+        /// <returns>The string representation.</returns>
+        public string ToString(string format, IFormatProvider formatProvider)
+        {
+            StringBuilder sb = new StringBuilder();
+            string separator = NumberFormatInfo.GetInstance(formatProvider).NumberGroupSeparator;
+            sb.Append('<');
+            sb.Append(this.X.ToString(format, formatProvider));
+            sb.Append(separator);
+            sb.Append(' ');
+            sb.Append(this.Y.ToString(format, formatProvider));
+            sb.Append('>');
+            return sb.ToString();
+        }
+
+        /// <summary>
+        /// Returns the length of the vector.
+        /// </summary>
+        /// <returns>The vector's length.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public float Length()
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                float ls = Vector2.Dot(this, this);
+                return (float)Math.Sqrt(ls);
+            }
+            else
+            {
+                float ls = X * X + Y * Y;
+                return (float)Math.Sqrt((double)ls);
+            }
+        }
+
+        /// <summary>
+        /// Returns the length of the vector squared. This operation is cheaper than Length().
+        /// </summary>
+        /// <returns>The vector's length squared.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public float LengthSquared()
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                return Vector2.Dot(this, this);
+            }
+            else
+            {
+                return X * X + Y * Y;
+            }
+        }
+        #endregion Public Instance Methods
+
+        #region Public Static Methods
+        /// <summary>
+        /// Returns the Euclidean distance between the two given points.
+        /// </summary>
+        /// <param name="value1">The first point.</param>
+        /// <param name="value2">The second point.</param>
+        /// <returns>The distance.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static float Distance(Vector2 value1, Vector2 value2)
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                Vector2 difference = value1 - value2;
+                float ls = Vector2.Dot(difference, difference);
+                return (float)System.Math.Sqrt(ls);
+            }
+            else
+            {
+                float dx = value1.X - value2.X;
+                float dy = value1.Y - value2.Y;
+
+                float ls = dx * dx + dy * dy;
+
+                return (float)Math.Sqrt((double)ls);
+            }
+        }
+
+        /// <summary>
+        /// Returns the Euclidean distance squared between the two given points.
+        /// </summary>
+        /// <param name="value1">The first point.</param>
+        /// <param name="value2">The second point.</param>
+        /// <returns>The distance squared.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static float DistanceSquared(Vector2 value1, Vector2 value2)
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                Vector2 difference = value1 - value2;
+                return Vector2.Dot(difference, difference);
+            }
+            else
+            {
+                float dx = value1.X - value2.X;
+                float dy = value1.Y - value2.Y;
+
+                return dx * dx + dy * dy;
+            }
+        }
+
+        /// <summary>
+        /// Returns a vector with the same direction as the given vector, but with a length of 1.
+        /// </summary>
+        /// <param name="value">The vector to normalize.</param>
+        /// <returns>The normalized vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Normalize(Vector2 value)
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                float length = value.Length();
+                return value / length;
+            }
+            else
+            {
+                float ls = value.X * value.X + value.Y * value.Y;
+                float invNorm = 1.0f / (float)Math.Sqrt((double)ls);
+
+                return new Vector2(
+                    value.X * invNorm,
+                    value.Y * invNorm);
+            }
+        }
+
+        /// <summary>
+        /// Returns the reflection of a vector off a surface that has the specified normal.
+        /// </summary>
+        /// <param name="vector">The source vector.</param>
+        /// <param name="normal">The normal of the surface being reflected off.</param>
+        /// <returns>The reflected vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Reflect(Vector2 vector, Vector2 normal)
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                float dot = Vector2.Dot(vector, normal);
+                return vector - (2 * dot * normal);
+            }
+            else
+            {
+                float dot = vector.X * normal.X + vector.Y * normal.Y;
+
+                return new Vector2(
+                    vector.X - 2.0f * dot * normal.X,
+                    vector.Y - 2.0f * dot * normal.Y);
+            }
+        }
+
+        /// <summary>
+        /// Restricts a vector between a min and max value.
+        /// </summary>
+        /// <param name="value1">The source vector.</param>
+        /// <param name="min">The minimum value.</param>
+        /// <param name="max">The maximum value.</param>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Clamp(Vector2 value1, Vector2 min, Vector2 max)
+        {
+            // This compare order is very important!!!
+            // We must follow HLSL behavior in the case user specified min value is bigger than max value.
+            float x = value1.X;
+            x = (x > max.X) ? max.X : x;
+            x = (x < min.X) ? min.X : x;
+
+            float y = value1.Y;
+            y = (y > max.Y) ? max.Y : y;
+            y = (y < min.Y) ? min.Y : y;
+
+            return new Vector2(x, y);
+        }
+
+        /// <summary>
+        /// Linearly interpolates between two vectors based on the given weighting.
+        /// </summary>
+        /// <param name="value1">The first source vector.</param>
+        /// <param name="value2">The second source vector.</param>
+        /// <param name="amount">Value between 0 and 1 indicating the weight of the second source vector.</param>
+        /// <returns>The interpolated vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Lerp(Vector2 value1, Vector2 value2, float amount)
+        {
+            return new Vector2(
+                value1.X + (value2.X - value1.X) * amount,
+                value1.Y + (value2.Y - value1.Y) * amount);
+        }
+
+        /// <summary>
+        /// Transforms a vector by the given matrix.
+        /// </summary>
+        /// <param name="position">The source vector.</param>
+        /// <param name="matrix">The transformation matrix.</param>
+        /// <returns>The transformed vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Transform(Vector2 position, Matrix3x2 matrix)
+        {
+            return new Vector2(
+                position.X * matrix.M11 + position.Y * matrix.M21 + matrix.M31,
+                position.X * matrix.M12 + position.Y * matrix.M22 + matrix.M32);
+        }
+
+        /// <summary>
+        /// Transforms a vector by the given matrix.
+        /// </summary>
+        /// <param name="position">The source vector.</param>
+        /// <param name="matrix">The transformation matrix.</param>
+        /// <returns>The transformed vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Transform(Vector2 position, Matrix4x4 matrix)
+        {
+            return new Vector2(
+                position.X * matrix.M11 + position.Y * matrix.M21 + matrix.M41,
+                position.X * matrix.M12 + position.Y * matrix.M22 + matrix.M42);
+        }
+
+        /// <summary>
+        /// Transforms a vector normal by the given matrix.
+        /// </summary>
+        /// <param name="normal">The source vector.</param>
+        /// <param name="matrix">The transformation matrix.</param>
+        /// <returns>The transformed vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 TransformNormal(Vector2 normal, Matrix3x2 matrix)
+        {
+            return new Vector2(
+                normal.X * matrix.M11 + normal.Y * matrix.M21,
+                normal.X * matrix.M12 + normal.Y * matrix.M22);
+        }
+
+        /// <summary>
+        /// Transforms a vector normal by the given matrix.
+        /// </summary>
+        /// <param name="normal">The source vector.</param>
+        /// <param name="matrix">The transformation matrix.</param>
+        /// <returns>The transformed vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 TransformNormal(Vector2 normal, Matrix4x4 matrix)
+        {
+            return new Vector2(
+                normal.X * matrix.M11 + normal.Y * matrix.M21,
+                normal.X * matrix.M12 + normal.Y * matrix.M22);
+        }
+
+        /// <summary>
+        /// Transforms a vector by the given Quaternion rotation value.
+        /// </summary>
+        /// <param name="value">The source vector to be rotated.</param>
+        /// <param name="rotation">The rotation to apply.</param>
+        /// <returns>The transformed vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Transform(Vector2 value, Quaternion rotation)
+        {
+            float x2 = rotation.X + rotation.X;
+            float y2 = rotation.Y + rotation.Y;
+            float z2 = rotation.Z + rotation.Z;
+
+            float wz2 = rotation.W * z2;
+            float xx2 = rotation.X * x2;
+            float xy2 = rotation.X * y2;
+            float yy2 = rotation.Y * y2;
+            float zz2 = rotation.Z * z2;
+
+            return new Vector2(
+                value.X * (1.0f - yy2 - zz2) + value.Y * (xy2 - wz2),
+                value.X * (xy2 + wz2) + value.Y * (1.0f - xx2 - zz2));
+        }
+        #endregion Public Static Methods
+
+        #region Public operator methods
+        // all the below methods should be inlined as they are 
+        // implemented over JIT intrinsics
+
+        /// <summary>
+        /// Adds two vectors together.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The summed vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Add(Vector2 left, Vector2 right)
+        {
+            return left + right;
+        }
+
+        /// <summary>
+        /// Subtracts the second vector from the first.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The difference vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Subtract(Vector2 left, Vector2 right)
+        {
+            return left - right;
+        }
+
+        /// <summary>
+        /// Multiplies two vectors together.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The product vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Multiply(Vector2 left, Vector2 right)
+        {
+            return left * right;
+        }
+
+        /// <summary>
+        /// Multiplies a vector by the given scalar.
+        /// </summary>
+        /// <param name="left">The source vector.</param>
+        /// <param name="right">The scalar value.</param>
+        /// <returns>The scaled vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Multiply(Vector2 left, Single right)
+        {
+            return left * right;
+        }
+
+        /// <summary>
+        /// Multiplies a vector by the given scalar.
+        /// </summary>
+        /// <param name="left">The scalar value.</param>
+        /// <param name="right">The source vector.</param>
+        /// <returns>The scaled vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Multiply(Single left, Vector2 right)
+        {
+            return left * right;
+        }
+
+        /// <summary>
+        /// Divides the first vector by the second.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The vector resulting from the division.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Divide(Vector2 left, Vector2 right)
+        {
+            return left / right;
+        }
+
+        /// <summary>
+        /// Divides the vector by the given scalar.
+        /// </summary>
+        /// <param name="left">The source vector.</param>
+        /// <param name="divisor">The scalar value.</param>
+        /// <returns>The result of the division.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Divide(Vector2 left, Single divisor)
+        {
+            return left / divisor;
+        }
+
+        /// <summary>
+        /// Negates a given vector.
+        /// </summary>
+        /// <param name="value">The source vector.</param>
+        /// <returns>The negated vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Negate(Vector2 value)
+        {
+            return -value;
+        }
+        #endregion Public operator methods
+    }
+}

mcs/class/referencesource/System.Numerics/System/Numerics/Vector2_Intrinsics.cs

@@ -0,0 +1,296 @@
+// Copyright (c) Microsoft. All rights reserved.
+// Licensed under the MIT license. See LICENSE file in the project root for full license information.
+
+using System.Runtime.CompilerServices;
+
+namespace System.Numerics
+{
+    // This file contains the definitions for all of the JIT intrinsic methods and properties that are recognized by the current x64 JIT compiler.
+    // The implementation defined here is used in any circumstance where the JIT fails to recognize these members as intrinsic.
+    // The JIT recognizes these methods and properties by name and signature: if either is changed, the JIT will no longer recognize the member.
+    // Some methods declared here are not strictly intrinsic, but delegate to an intrinsic method. For example, only one overload of CopyTo() 
+
+    public partial struct Vector2
+    {
+        /// <summary>
+        /// The X component of the vector.
+        /// </summary>
+        public Single X;
+        /// <summary>
+        /// The Y component of the vector.
+        /// </summary>
+        public Single Y;
+
+        #region Constructors
+        /// <summary>
+        /// Constructs a vector whose elements are all the single specified value.
+        /// </summary>
+        /// <param name="value">The element to fill the vector with.</param>
+        [JitIntrinsic]
+        public Vector2(Single value) : this(value, value) { }
+
+        /// <summary>
+        /// Constructs a vector with the given individual elements.
+        /// </summary>
+        /// <param name="x">The X component.</param>
+        /// <param name="y">The Y component.</param>
+        [JitIntrinsic]
+        public Vector2(Single x, Single y)
+        {
+            X = x;
+            Y = y;
+        }
+        #endregion Constructors
+
+        #region Public Instance Methods
+        /// <summary>
+        /// Copies the contents of the vector into the given array.
+        /// </summary>
+        /// <param name="array">The destination array.</param>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public void CopyTo(Single[] array)
+        {
+            CopyTo(array, 0);
+        }
+
+        /// <summary>
+        /// Copies the contents of the vector into the given array, starting from the given index.
+        /// </summary>
+        /// <exception cref="ArgumentNullException">If array is null.</exception>
+        /// <exception cref="RankException">If array is multidimensional.</exception>
+        /// <exception cref="ArgumentOutOfRangeException">If index is greater than end of the array or index is less than zero.</exception>
+        /// <exception cref="ArgumentException">If number of elements in source vector is greater than those available in destination array
+        /// or if there are not enough elements to copy.</exception>
+        public void CopyTo(Single[] array, int index)
+        {
+            if (array == null)
+            {
+                // Match the JIT's exception type here. For perf, a NullReference is thrown instead of an ArgumentNull.
+                throw new NullReferenceException(SR.GetString("Arg_NullArgumentNullRef"));
+            }
+            if (index < 0 || index >= array.Length)
+            {
+                throw new ArgumentOutOfRangeException(SR.GetString("Arg_ArgumentOutOfRangeException", index));
+            }
+            if ((array.Length - index) < 2)
+            {
+                throw new ArgumentException(SR.GetString("Arg_ElementsInSourceIsGreaterThanDestination", index));
+            }
+            array[index] = X;
+            array[index + 1] = Y;
+        }
+
+        /// <summary>
+        /// Returns a boolean indicating whether the given Vector2 is equal to this Vector2 instance.
+        /// </summary>
+        /// <param name="other">The Vector2 to compare this instance to.</param>
+        /// <returns>True if the other Vector2 is equal to this instance; False otherwise.</returns>
+        [JitIntrinsic]
+        public bool Equals(Vector2 other)
+        {
+            return this.X == other.X && this.Y == other.Y;
+        }
+        #endregion Public Instance Methods
+
+        #region Public Static Methods
+        /// <summary>
+        /// Returns the dot product of two vectors.
+        /// </summary>
+        /// <param name="value1">The first vector.</param>
+        /// <param name="value2">The second vector.</param>
+        /// <returns>The dot product.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static float Dot(Vector2 value1, Vector2 value2)
+        {
+            return value1.X * value2.X +
+                   value1.Y * value2.Y;
+        }
+
+        /// <summary>
+        /// Returns a vector whose elements are the minimum of each of the pairs of elements in the two source vectors.
+        /// </summary>
+        /// <param name="value1">The first source vector.</param>
+        /// <param name="value2">The second source vector.</param>
+        /// <returns>The minimized vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Min(Vector2 value1, Vector2 value2)
+        {
+            return new Vector2(
+                (value1.X < value2.X) ? value1.X : value2.X,
+                (value1.Y < value2.Y) ? value1.Y : value2.Y);
+        }
+
+        /// <summary>
+        /// Returns a vector whose elements are the maximum of each of the pairs of elements in the two source vectors
+        /// </summary>
+        /// <param name="value1">The first source vector</param>
+        /// <param name="value2">The second source vector</param>
+        /// <returns>The maximized vector</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Max(Vector2 value1, Vector2 value2)
+        {
+            return new Vector2(
+                (value1.X > value2.X) ? value1.X : value2.X,
+                (value1.Y > value2.Y) ? value1.Y : value2.Y);
+        }
+
+        /// <summary>
+        /// Returns a vector whose elements are the absolute values of each of the source vector's elements.
+        /// </summary>
+        /// <param name="value">The source vector.</param>
+        /// <returns>The absolute value vector.</returns>        
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 Abs(Vector2 value)
+        {
+            return new Vector2(Math.Abs(value.X), Math.Abs(value.Y));
+        }
+
+        /// <summary>
+        /// Returns a vector whose elements are the square root of each of the source vector's elements.
+        /// </summary>
+        /// <param name="value">The source vector.</param>
+        /// <returns>The square root vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 SquareRoot(Vector2 value)
+        {
+            return new Vector2((Single)Math.Sqrt(value.X), (Single)Math.Sqrt(value.Y));
+        }
+        #endregion Public Static Methods
+
+        #region Public Static Operators
+        /// <summary>
+        /// Adds two vectors together.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The summed vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 operator +(Vector2 left, Vector2 right)
+        {
+            return new Vector2(left.X + right.X, left.Y + right.Y);
+        }
+
+        /// <summary>
+        /// Subtracts the second vector from the first.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The difference vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 operator -(Vector2 left, Vector2 right)
+        {
+            return new Vector2(left.X - right.X, left.Y - right.Y);
+        }
+
+        /// <summary>
+        /// Multiplies two vectors together.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The product vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 operator *(Vector2 left, Vector2 right)
+        {
+            return new Vector2(left.X * right.X, left.Y * right.Y);
+        }
+
+        /// <summary>
+        /// Multiplies a vector by the given scalar.
+        /// </summary>
+        /// <param name="left">The scalar value.</param>
+        /// <param name="right">The source vector.</param>
+        /// <returns>The scaled vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 operator *(Single left, Vector2 right)
+        {
+            return new Vector2(left, left) * right;
+        }
+
+        /// <summary>
+        /// Multiplies a vector by the given scalar.
+        /// </summary>
+        /// <param name="left">The source vector.</param>
+        /// <param name="right">The scalar value.</param>
+        /// <returns>The scaled vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 operator *(Vector2 left, Single right)
+        {
+            return left * new Vector2(right, right);
+        }
+
+        /// <summary>
+        /// Divides the first vector by the second.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The vector resulting from the division.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 operator /(Vector2 left, Vector2 right)
+        {
+            return new Vector2(left.X / right.X, left.Y / right.Y);
+        }
+
+        /// <summary>
+        /// Divides the vector by the given scalar.
+        /// </summary>
+        /// <param name="value1">The source vector.</param>
+        /// <param name="value2">The scalar value.</param>
+        /// <returns>The result of the division.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 operator /(Vector2 value1, float value2)
+        {
+            float invDiv = 1.0f / value2;
+            return new Vector2(
+                value1.X * invDiv,
+                value1.Y * invDiv);
+        }
+
+        /// <summary>
+        /// Negates a given vector.
+        /// </summary>
+        /// <param name="value">The source vector.</param>
+        /// <returns>The negated vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector2 operator -(Vector2 value)
+        {
+            return Zero - value;
+        }
+
+        /// <summary>
+        /// Returns a boolean indicating whether the two given vectors are equal.
+        /// </summary>
+        /// <param name="left">The first vector to compare.</param>
+        /// <param name="right">The second vector to compare.</param>
+        /// <returns>True if the vectors are equal; False otherwise.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static bool operator ==(Vector2 left, Vector2 right)
+        {
+            return left.Equals(right);
+        }
+
+        /// <summary>
+        /// Returns a boolean indicating whether the two given vectors are not equal.
+        /// </summary>
+        /// <param name="left">The first vector to compare.</param>
+        /// <param name="right">The second vector to compare.</param>
+        /// <returns>True if the vectors are not equal; False if they are equal.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static bool operator !=(Vector2 left, Vector2 right)
+        {
+            return !(left == right);
+        }
+        #endregion Public Static Operators
+    }
+}

mcs/class/referencesource/System.Numerics/System/Numerics/Vector3.cs

@@ -0,0 +1,471 @@
+// Copyright (c) Microsoft. All rights reserved.
+// Licensed under the MIT license. See LICENSE file in the project root for full license information.
+
+using System.Globalization;
+using System.Runtime.CompilerServices;
+using System.Text;
+
+namespace System.Numerics
+{
+    /// <summary>
+    /// A structure encapsulating three single precision floating point values and provides hardware accelerated methods.
+    /// </summary>
+    public partial struct Vector3 : IEquatable<Vector3>, IFormattable
+    {
+        #region Public Static Properties
+        /// <summary>
+        /// Returns the vector (0,0,0).
+        /// </summary>
+        public static Vector3 Zero { get { return new Vector3(); } }
+        /// <summary>
+        /// Returns the vector (1,1,1).
+        /// </summary>
+        public static Vector3 One { get { return new Vector3(1.0f, 1.0f, 1.0f); } }
+        /// <summary>
+        /// Returns the vector (1,0,0).
+        /// </summary>
+        public static Vector3 UnitX { get { return new Vector3(1.0f, 0.0f, 0.0f); } }
+        /// <summary>
+        /// Returns the vector (0,1,0).
+        /// </summary>
+        public static Vector3 UnitY { get { return new Vector3(0.0f, 1.0f, 0.0f); } }
+        /// <summary>
+        /// Returns the vector (0,0,1).
+        /// </summary>
+        public static Vector3 UnitZ { get { return new Vector3(0.0f, 0.0f, 1.0f); } }
+        #endregion Public Static Properties
+
+        #region Public Instance Methods
+
+        /// <summary>
+        /// Returns the hash code for this instance.
+        /// </summary>
+        /// <returns>The hash code.</returns>
+        public override int GetHashCode()
+        {
+            int hash = this.X.GetHashCode();
+            hash = HashCodeHelper.CombineHashCodes(hash, this.Y.GetHashCode());
+            hash = HashCodeHelper.CombineHashCodes(hash, this.Z.GetHashCode());
+            return hash;
+        }
+
+        /// <summary>
+        /// Returns a boolean indicating whether the given Object is equal to this Vector3 instance.
+        /// </summary>
+        /// <param name="obj">The Object to compare against.</param>
+        /// <returns>True if the Object is equal to this Vector3; False otherwise.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public override bool Equals(object obj)
+        {
+            if (!(obj is Vector3))
+                return false;
+            return Equals((Vector3)obj);
+        }
+
+        /// <summary>
+        /// Returns a String representing this Vector3 instance.
+        /// </summary>
+        /// <returns>The string representation.</returns>
+        public override string ToString()
+        {
+            return ToString("G", CultureInfo.CurrentCulture);
+        }
+
+        /// <summary>
+        /// Returns a String representing this Vector3 instance, using the specified format to format individual elements.
+        /// </summary>
+        /// <param name="format">The format of individual elements.</param>
+        /// <returns>The string representation.</returns>
+        public string ToString(string format)
+        {
+            return ToString(format, CultureInfo.CurrentCulture);
+        }
+
+        /// <summary>
+        /// Returns a String representing this Vector3 instance, using the specified format to format individual elements 
+        /// and the given IFormatProvider.
+        /// </summary>
+        /// <param name="format">The format of individual elements.</param>
+        /// <param name="formatProvider">The format provider to use when formatting elements.</param>
+        /// <returns>The string representation.</returns>
+        public string ToString(string format, IFormatProvider formatProvider)
+        {
+            StringBuilder sb = new StringBuilder();
+            string separator = NumberFormatInfo.GetInstance(formatProvider).NumberGroupSeparator;
+            sb.Append('<');
+            sb.Append(((IFormattable)this.X).ToString(format, formatProvider));
+            sb.Append(separator);
+            sb.Append(' ');
+            sb.Append(((IFormattable)this.Y).ToString(format, formatProvider));
+            sb.Append(separator);
+            sb.Append(' ');
+            sb.Append(((IFormattable)this.Z).ToString(format, formatProvider));
+            sb.Append('>');
+            return sb.ToString();
+        }
+
+        /// <summary>
+        /// Returns the length of the vector.
+        /// </summary>
+        /// <returns>The vector's length.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public float Length()
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                float ls = Vector3.Dot(this, this);
+                return (float)System.Math.Sqrt(ls);
+            }
+            else
+            {
+                float ls = X * X + Y * Y + Z * Z;
+                return (float)System.Math.Sqrt(ls);
+            }
+        }
+
+        /// <summary>
+        /// Returns the length of the vector squared. This operation is cheaper than Length().
+        /// </summary>
+        /// <returns>The vector's length squared.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public float LengthSquared()
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                return Vector3.Dot(this, this);
+            }
+            else
+            {
+                return X * X + Y * Y + Z * Z;
+            }
+        }
+        #endregion Public Instance Methods
+
+        #region Public Static Methods
+        /// <summary>
+        /// Returns the Euclidean distance between the two given points.
+        /// </summary>
+        /// <param name="value1">The first point.</param>
+        /// <param name="value2">The second point.</param>
+        /// <returns>The distance.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static float Distance(Vector3 value1, Vector3 value2)
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                Vector3 difference = value1 - value2;
+                float ls = Vector3.Dot(difference, difference);
+                return (float)System.Math.Sqrt(ls);
+            }
+            else
+            {
+                float dx = value1.X - value2.X;
+                float dy = value1.Y - value2.Y;
+                float dz = value1.Z - value2.Z;
+
+                float ls = dx * dx + dy * dy + dz * dz;
+
+                return (float)System.Math.Sqrt((double)ls);
+            }
+        }
+
+        /// <summary>
+        /// Returns the Euclidean distance squared between the two given points.
+        /// </summary>
+        /// <param name="value1">The first point.</param>
+        /// <param name="value2">The second point.</param>
+        /// <returns>The distance squared.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static float DistanceSquared(Vector3 value1, Vector3 value2)
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                Vector3 difference = value1 - value2;
+                return Vector3.Dot(difference, difference);
+            }
+            else
+            {
+                float dx = value1.X - value2.X;
+                float dy = value1.Y - value2.Y;
+                float dz = value1.Z - value2.Z;
+
+                return dx * dx + dy * dy + dz * dz;
+            }
+        }
+
+        /// <summary>
+        /// Returns a vector with the same direction as the given vector, but with a length of 1.
+        /// </summary>
+        /// <param name="value">The vector to normalize.</param>
+        /// <returns>The normalized vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Normalize(Vector3 value)
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                float length = value.Length();
+                return value / length;
+            }
+            else
+            {
+                float ls = value.X * value.X + value.Y * value.Y + value.Z * value.Z;
+                float length = (float)System.Math.Sqrt(ls);
+                return new Vector3(value.X / length, value.Y / length, value.Z / length);
+            }
+        }
+
+        /// <summary>
+        /// Computes the cross product of two vectors.
+        /// </summary>
+        /// <param name="vector1">The first vector.</param>
+        /// <param name="vector2">The second vector.</param>
+        /// <returns>The cross product.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Cross(Vector3 vector1, Vector3 vector2)
+        {
+            return new Vector3(
+                vector1.Y * vector2.Z - vector1.Z * vector2.Y,
+                vector1.Z * vector2.X - vector1.X * vector2.Z,
+                vector1.X * vector2.Y - vector1.Y * vector2.X);
+        }
+
+        /// <summary>
+        /// Returns the reflection of a vector off a surface that has the specified normal.
+        /// </summary>
+        /// <param name="vector">The source vector.</param>
+        /// <param name="normal">The normal of the surface being reflected off.</param>
+        /// <returns>The reflected vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Reflect(Vector3 vector, Vector3 normal)
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                float dot = Vector3.Dot(vector, normal);
+                Vector3 temp = normal * dot * 2f;
+                return vector - temp;
+            }
+            else
+            {
+                float dot = vector.X * normal.X + vector.Y * normal.Y + vector.Z * normal.Z;
+                float tempX = normal.X * dot * 2f;
+                float tempY = normal.Y * dot * 2f;
+                float tempZ = normal.Z * dot * 2f;
+                return new Vector3(vector.X - tempX, vector.Y - tempY, vector.Z - tempZ);
+            }
+        }
+
+        /// <summary>
+        /// Restricts a vector between a min and max value.
+        /// </summary>
+        /// <param name="value1">The source vector.</param>
+        /// <param name="min">The minimum value.</param>
+        /// <param name="max">The maximum value.</param>
+        /// <returns>The restricted vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Clamp(Vector3 value1, Vector3 min, Vector3 max)
+        {
+            // This compare order is very important!!!
+            // We must follow HLSL behavior in the case user specified min value is bigger than max value.
+
+            float x = value1.X;
+            x = (x > max.X) ? max.X : x;
+            x = (x < min.X) ? min.X : x;
+
+            float y = value1.Y;
+            y = (y > max.Y) ? max.Y : y;
+            y = (y < min.Y) ? min.Y : y;
+
+            float z = value1.Z;
+            z = (z > max.Z) ? max.Z : z;
+            z = (z < min.Z) ? min.Z : z;
+
+            return new Vector3(x, y, z);
+        }
+
+        /// <summary>
+        /// Linearly interpolates between two vectors based on the given weighting.
+        /// </summary>
+        /// <param name="value1">The first source vector.</param>
+        /// <param name="value2">The second source vector.</param>
+        /// <param name="amount">Value between 0 and 1 indicating the weight of the second source vector.</param>
+        /// <returns>The interpolated vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Lerp(Vector3 value1, Vector3 value2, float amount)
+        {
+            if (Vector.IsHardwareAccelerated)
+            {
+                Vector3 firstInfluence = value1 * (1f - amount);
+                Vector3 secondInfluence = value2 * amount;
+                return firstInfluence + secondInfluence;
+            }
+            else
+            {
+                return new Vector3(
+                    value1.X + (value2.X - value1.X) * amount,
+                    value1.Y + (value2.Y - value1.Y) * amount,
+                    value1.Z + (value2.Z - value1.Z) * amount);
+            }
+        }
+
+        /// <summary>
+        /// Transforms a vector by the given matrix.
+        /// </summary>
+        /// <param name="position">The source vector.</param>
+        /// <param name="matrix">The transformation matrix.</param>
+        /// <returns>The transformed vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Transform(Vector3 position, Matrix4x4 matrix)
+        {
+            return new Vector3(
+                position.X * matrix.M11 + position.Y * matrix.M21 + position.Z * matrix.M31 + matrix.M41,
+                position.X * matrix.M12 + position.Y * matrix.M22 + position.Z * matrix.M32 + matrix.M42,
+                position.X * matrix.M13 + position.Y * matrix.M23 + position.Z * matrix.M33 + matrix.M43);
+        }
+
+        /// <summary>
+        /// Transforms a vector normal by the given matrix.
+        /// </summary>
+        /// <param name="normal">The source vector.</param>
+        /// <param name="matrix">The transformation matrix.</param>
+        /// <returns>The transformed vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 TransformNormal(Vector3 normal, Matrix4x4 matrix)
+        {
+            return new Vector3(
+                normal.X * matrix.M11 + normal.Y * matrix.M21 + normal.Z * matrix.M31,
+                normal.X * matrix.M12 + normal.Y * matrix.M22 + normal.Z * matrix.M32,
+                normal.X * matrix.M13 + normal.Y * matrix.M23 + normal.Z * matrix.M33);
+        }
+
+        /// <summary>
+        /// Transforms a vector by the given Quaternion rotation value.
+        /// </summary>
+        /// <param name="value">The source vector to be rotated.</param>
+        /// <param name="rotation">The rotation to apply.</param>
+        /// <returns>The transformed vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Transform(Vector3 value, Quaternion rotation)
+        {
+            float x2 = rotation.X + rotation.X;
+            float y2 = rotation.Y + rotation.Y;
+            float z2 = rotation.Z + rotation.Z;
+
+            float wx2 = rotation.W * x2;
+            float wy2 = rotation.W * y2;
+            float wz2 = rotation.W * z2;
+            float xx2 = rotation.X * x2;
+            float xy2 = rotation.X * y2;
+            float xz2 = rotation.X * z2;
+            float yy2 = rotation.Y * y2;
+            float yz2 = rotation.Y * z2;
+            float zz2 = rotation.Z * z2;
+
+            return new Vector3(
+                value.X * (1.0f - yy2 - zz2) + value.Y * (xy2 - wz2) + value.Z * (xz2 + wy2),
+                value.X * (xy2 + wz2) + value.Y * (1.0f - xx2 - zz2) + value.Z * (yz2 - wx2),
+                value.X * (xz2 - wy2) + value.Y * (yz2 + wx2) + value.Z * (1.0f - xx2 - yy2));
+        }
+        #endregion Public Static Methods
+
+        #region Public operator methods
+
+        // All these methods should be inlined as they are implemented
+        // over JIT intrinsics
+
+        /// <summary>
+        /// Adds two vectors together.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The summed vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Add(Vector3 left, Vector3 right)
+        {
+            return left + right;
+        }
+
+        /// <summary>
+        /// Subtracts the second vector from the first.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The difference vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Subtract(Vector3 left, Vector3 right)
+        {
+            return left - right;
+        }
+
+        /// <summary>
+        /// Multiplies two vectors together.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The product vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Multiply(Vector3 left, Vector3 right)
+        {
+            return left * right;
+        }
+
+        /// <summary>
+        /// Multiplies a vector by the given scalar.
+        /// </summary>
+        /// <param name="left">The source vector.</param>
+        /// <param name="right">The scalar value.</param>
+        /// <returns>The scaled vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Multiply(Vector3 left, Single right)
+        {
+            return left * right;
+        }
+
+        /// <summary>
+        /// Multiplies a vector by the given scalar.
+        /// </summary>
+        /// <param name="left">The scalar value.</param>
+        /// <param name="right">The source vector.</param>
+        /// <returns>The scaled vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Multiply(Single left, Vector3 right)
+        {
+            return left * right;
+        }
+
+        /// <summary>
+        /// Divides the first vector by the second.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The vector resulting from the division.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Divide(Vector3 left, Vector3 right)
+        {
+            return left / right;
+        }
+
+        /// <summary>
+        /// Divides the vector by the given scalar.
+        /// </summary>
+        /// <param name="left">The source vector.</param>
+        /// <param name="divisor">The scalar value.</param>
+        /// <returns>The result of the division.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Divide(Vector3 left, Single divisor)
+        {
+            return left / divisor;
+        }
+
+        /// <summary>
+        /// Negates a given vector.
+        /// </summary>
+        /// <param name="value">The source vector.</param>
+        /// <returns>The negated vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Negate(Vector3 value)
+        {
+            return -value;
+        }
+        #endregion Public operator methods
+    }
+}

mcs/class/referencesource/System.Numerics/System/Numerics/Vector3_Intrinsics.cs

@@ -0,0 +1,322 @@
+// Copyright (c) Microsoft. All rights reserved.
+// Licensed under the MIT license. See LICENSE file in the project root for full license information.
+
+using System.Runtime.CompilerServices;
+
+namespace System.Numerics
+{
+    // This file contains the definitions for all of the JIT intrinsic methods and properties that are recognized by the current x64 JIT compiler.
+    // The implementation defined here is used in any circumstance where the JIT fails to recognize these members as intrinsic.
+    // The JIT recognizes these methods and properties by name and signature: if either is changed, the JIT will no longer recognize the member.
+    // Some methods declared here are not strictly intrinsic, but delegate to an intrinsic method. For example, only one overload of CopyTo()
+    // is actually recognized by the JIT, but both are here for simplicity.
+
+    public partial struct Vector3
+    {
+        /// <summary>
+        /// The X component of the vector.
+        /// </summary>
+        public Single X;
+        /// <summary>
+        /// The Y component of the vector.
+        /// </summary>
+        public Single Y;
+        /// <summary>
+        /// The Z component of the vector.
+        /// </summary>
+        public Single Z;
+
+        #region Constructors
+        /// <summary>
+        /// Constructs a vector whose elements are all the single specified value.
+        /// </summary>
+        /// <param name="value">The element to fill the vector with.</param>
+        [JitIntrinsic]
+        public Vector3(Single value) : this(value, value, value) { }
+
+        /// <summary>
+        /// Constructs a Vector3 from the given Vector2 and a third value.
+        /// </summary>
+        /// <param name="value">The Vector to extract X and Y components from.</param>
+        /// <param name="z">The Z component.</param>
+        public Vector3(Vector2 value, float z) : this(value.X, value.Y, z) { }
+
+        /// <summary>
+        /// Constructs a vector with the given individual elements.
+        /// </summary>
+        /// <param name="x">The X component.</param>
+        /// <param name="y">The Y component.</param>
+        /// <param name="z">The Z component.</param>
+        [JitIntrinsic]
+        public Vector3(Single x, Single y, Single z)
+        {
+            X = x;
+            Y = y;
+            Z = z;
+        }
+        #endregion Constructors
+
+        #region Public Instance Methods
+        /// <summary>
+        /// Copies the contents of the vector into the given array.
+        /// </summary>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public void CopyTo(Single[] array)
+        {
+            CopyTo(array, 0);
+        }
+
+        /// <summary>
+        /// Copies the contents of the vector into the given array, starting from index.
+        /// </summary>
+        /// <exception cref="ArgumentNullException">If array is null.</exception>
+        /// <exception cref="RankException">If array is multidimensional.</exception>
+        /// <exception cref="ArgumentOutOfRangeException">If index is greater than end of the array or index is less than zero.</exception>
+        /// <exception cref="ArgumentException">If number of elements in source vector is greater than those available in destination array.</exception>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public void CopyTo(Single[] array, int index)
+        {
+            if (array == null)
+            {
+                // Match the JIT's exception type here. For perf, a NullReference is thrown instead of an ArgumentNull.
+                throw new NullReferenceException(SR.GetString("Arg_NullArgumentNullRef"));
+            }
+            if (index < 0 || index >= array.Length)
+            {
+                throw new ArgumentOutOfRangeException(SR.GetString("Arg_ArgumentOutOfRangeException", index));
+            }
+            if ((array.Length - index) < 3)
+            {
+                throw new ArgumentException(SR.GetString("Arg_ElementsInSourceIsGreaterThanDestination", index));
+            }
+            array[index] = X;
+            array[index + 1] = Y;
+            array[index + 2] = Z;
+        }
+
+        /// <summary>
+        /// Returns a boolean indicating whether the given Vector3 is equal to this Vector3 instance.
+        /// </summary>
+        /// <param name="other">The Vector3 to compare this instance to.</param>
+        /// <returns>True if the other Vector3 is equal to this instance; False otherwise.</returns>
+        [JitIntrinsic]
+        public bool Equals(Vector3 other)
+        {
+            return X == other.X &&
+                   Y == other.Y &&
+                   Z == other.Z;
+        }
+        #endregion Public Instance Methods
+
+        #region Public Static Methods
+        /// <summary>
+        /// Returns the dot product of two vectors.
+        /// </summary>
+        /// <param name="vector1">The first vector.</param>
+        /// <param name="vector2">The second vector.</param>
+        /// <returns>The dot product.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static float Dot(Vector3 vector1, Vector3 vector2)
+        {
+            return vector1.X * vector2.X +
+                   vector1.Y * vector2.Y +
+                   vector1.Z * vector2.Z;
+        }
+
+        /// <summary>
+        /// Returns a vector whose elements are the minimum of each of the pairs of elements in the two source vectors.
+        /// </summary>
+        /// <param name="value1">The first source vector.</param>
+        /// <param name="value2">The second source vector.</param>
+        /// <returns>The minimized vector.</returns>
+        [JitIntrinsic]
+        public static Vector3 Min(Vector3 value1, Vector3 value2)
+        {
+            return new Vector3(
+                (value1.X < value2.X) ? value1.X : value2.X,
+                (value1.Y < value2.Y) ? value1.Y : value2.Y,
+                (value1.Z < value2.Z) ? value1.Z : value2.Z);
+        }
+
+        /// <summary>
+        /// Returns a vector whose elements are the maximum of each of the pairs of elements in the two source vectors.
+        /// </summary>
+        /// <param name="value1">The first source vector.</param>
+        /// <param name="value2">The second source vector.</param>
+        /// <returns>The maximized vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Max(Vector3 value1, Vector3 value2)
+        {
+            return new Vector3(
+                (value1.X > value2.X) ? value1.X : value2.X,
+                (value1.Y > value2.Y) ? value1.Y : value2.Y,
+                (value1.Z > value2.Z) ? value1.Z : value2.Z);
+        }
+
+        /// <summary>
+        /// Returns a vector whose elements are the absolute values of each of the source vector's elements.
+        /// </summary>
+        /// <param name="value">The source vector.</param>
+        /// <returns>The absolute value vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 Abs(Vector3 value)
+        {
+            return new Vector3(Math.Abs(value.X), Math.Abs(value.Y), Math.Abs(value.Z));
+        }
+
+        /// <summary>
+        /// Returns a vector whose elements are the square root of each of the source vector's elements.
+        /// </summary>
+        /// <param name="value">The source vector.</param>
+        /// <returns>The square root vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 SquareRoot(Vector3 value)
+        {
+            return new Vector3((Single)Math.Sqrt(value.X), (Single)Math.Sqrt(value.Y), (Single)Math.Sqrt(value.Z));
+        }
+        #endregion Public Static Methods
+
+        #region Public Static Operators
+        /// <summary>
+        /// Adds two vectors together.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The summed vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 operator +(Vector3 left, Vector3 right)
+        {
+            return new Vector3(left.X + right.X, left.Y + right.Y, left.Z + right.Z);
+        }
+
+        /// <summary>
+        /// Subtracts the second vector from the first.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The difference vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 operator -(Vector3 left, Vector3 right)
+        {
+            return new Vector3(left.X - right.X, left.Y - right.Y, left.Z - right.Z);
+        }
+
+        /// <summary>
+        /// Multiplies two vectors together.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The product vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 operator *(Vector3 left, Vector3 right)
+        {
+            return new Vector3(left.X * right.X, left.Y * right.Y, left.Z * right.Z);
+        }
+
+        /// <summary>
+        /// Multiplies a vector by the given scalar.
+        /// </summary>
+        /// <param name="left">The source vector.</param>
+        /// <param name="right">The scalar value.</param>
+        /// <returns>The scaled vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 operator *(Vector3 left, Single right)
+        {
+            return left * new Vector3(right);
+        }
+
+        /// <summary>
+        /// Multiplies a vector by the given scalar.
+        /// </summary>
+        /// <param name="left">The scalar value.</param>
+        /// <param name="right">The source vector.</param>
+        /// <returns>The scaled vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 operator *(Single left, Vector3 right)
+        {
+            return new Vector3(left) * right;
+        }
+
+        /// <summary>
+        /// Divides the first vector by the second.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The vector resulting from the division.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 operator /(Vector3 left, Vector3 right)
+        {
+            return new Vector3(left.X / right.X, left.Y / right.Y, left.Z / right.Z);
+        }
+
+        /// <summary>
+        /// Divides the vector by the given scalar.
+        /// </summary>
+        /// <param name="value1">The source vector.</param>
+        /// <param name="value2">The scalar value.</param>
+        /// <returns>The result of the division.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 operator /(Vector3 value1, float value2)
+        {
+            float invDiv = 1.0f / value2;
+
+            return new Vector3(
+                value1.X * invDiv,
+                value1.Y * invDiv,
+                value1.Z * invDiv);
+        }
+
+        /// <summary>
+        /// Negates a given vector.
+        /// </summary>
+        /// <param name="value">The source vector.</param>
+        /// <returns>The negated vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector3 operator -(Vector3 value)
+        {
+            return Zero - value;
+        }
+
+        /// <summary>
+        /// Returns a boolean indicating whether the two given vectors are equal.
+        /// </summary>
+        /// <param name="left">The first vector to compare.</param>
+        /// <param name="right">The second vector to compare.</param>
+        /// <returns>True if the vectors are equal; False otherwise.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static bool operator ==(Vector3 left, Vector3 right)
+        {
+            return (left.X == right.X &&
+                    left.Y == right.Y &&
+                    left.Z == right.Z);
+        }
+
+        /// <summary>
+        /// Returns a boolean indicating whether the two given vectors are not equal.
+        /// </summary>
+        /// <param name="left">The first vector to compare.</param>
+        /// <param name="right">The second vector to compare.</param>
+        /// <returns>True if the vectors are not equal; False if they are equal.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static bool operator !=(Vector3 left, Vector3 right)
+        {
+            return (left.X != right.X ||
+                    left.Y != right.Y ||
+                    left.Z != right.Z);
+        }
+        #endregion Public Static Operators
+    }
+}

mcs/class/referencesource/System.Numerics/System/Numerics/Vector4_Intrinsics.cs

@@ -0,0 +1,353 @@
+// Copyright (c) Microsoft. All rights reserved.
+// Licensed under the MIT license. See LICENSE file in the project root for full license information.
+
+using System.Runtime.CompilerServices;
+
+namespace System.Numerics
+{
+    // This file contains the definitions for all of the JIT intrinsic methods and properties that are recognized by the current x64 JIT compiler.
+    // The implementation defined here is used in any circumstance where the JIT fails to recognize these members as intrinsic.
+    // The JIT recognizes these methods and properties by name and signature: if either is changed, the JIT will no longer recognize the member.
+    // Some methods declared here are not strictly intrinsic, but delegate to an intrinsic method. For example, only one overload of CopyTo() 
+
+    public partial struct Vector4
+    {
+        /// <summary>
+        /// The X component of the vector.
+        /// </summary>
+        public Single X;
+        /// <summary>
+        /// The Y component of the vector.
+        /// </summary>
+        public Single Y;
+        /// <summary>
+        /// The Z component of the vector.
+        /// </summary>
+        public Single Z;
+        /// <summary>
+        /// The W component of the vector.
+        /// </summary>
+        public Single W;
+
+        #region Constructors
+
+        /// <summary>
+        /// Constructs a vector whose elements are all the single specified value.
+        /// </summary>
+        /// <param name="value">The element to fill the vector with.</param>
+        [JitIntrinsic]
+        public Vector4(Single value)
+            : this(value, value, value, value)
+        {
+        }
+        /// <summary>
+        /// Constructs a vector with the given individual elements.
+        /// </summary>
+        /// <param name="w">W component.</param>
+        /// <param name="x">X component.</param>
+        /// <param name="y">Y component.</param>
+        /// <param name="z">Z component.</param>
+        [JitIntrinsic]
+        public Vector4(Single x, Single y, Single z, Single w)
+        {
+            W = w;
+            X = x;
+            Y = y;
+            Z = z;
+        }
+
+        /// <summary>
+        /// Constructs a Vector4 from the given Vector2 and a Z and W component.
+        /// </summary>
+        /// <param name="value">The vector to use as the X and Y components.</param>
+        /// <param name="z">The Z component.</param>
+        /// <param name="w">The W component.</param>
+        public Vector4(Vector2 value, Single z, Single w)
+        {
+            X = value.X;
+            Y = value.Y;
+            Z = z;
+            W = w;
+        }
+
+        /// <summary>
+        /// Constructs a Vector4 from the given Vector3 and a W component.
+        /// </summary>
+        /// <param name="value">The vector to use as the X, Y, and Z components.</param>
+        /// <param name="w">The W component.</param>
+        public Vector4(Vector3 value, Single w)
+        {
+            X = value.X;
+            Y = value.Y;
+            Z = value.Z;
+            W = w;
+        }
+        #endregion Constructors
+
+        #region Public Instance Methods
+        /// <summary>
+        /// Copies the contents of the vector into the given array.
+        /// </summary>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public void CopyTo(Single[] array)
+        {
+            CopyTo(array, 0);
+        }
+
+        /// <summary>
+        /// Copies the contents of the vector into the given array, starting from index.
+        /// </summary>
+        /// <exception cref="ArgumentNullException">If array is null.</exception>
+        /// <exception cref="RankException">If array is multidimensional.</exception>
+        /// <exception cref="ArgumentOutOfRangeException">If index is greater than end of the array or index is less than zero.</exception>
+        /// <exception cref="ArgumentException">If number of elements in source vector is greater than those available in destination array.</exception>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public void CopyTo(Single[] array, int index)
+        {
+            if (array == null)
+            {
+                // Match the JIT's exception type here. For perf, a NullReference is thrown instead of an ArgumentNull.
+                throw new NullReferenceException(SR.GetString("Arg_NullArgumentNullRef"));
+            }
+            if (index < 0 || index >= array.Length)
+            {
+                throw new ArgumentOutOfRangeException(SR.GetString("Arg_ArgumentOutOfRangeException", index));
+            }
+            if ((array.Length - index) < 4)
+            {
+                throw new ArgumentException(SR.GetString("Arg_ElementsInSourceIsGreaterThanDestination", index));
+            }
+            array[index] = X;
+            array[index + 1] = Y;
+            array[index + 2] = Z;
+            array[index + 3] = W;
+        }
+
+        /// <summary>
+        /// Returns a boolean indicating whether the given Vector4 is equal to this Vector4 instance.
+        /// </summary>
+        /// <param name="other">The Vector4 to compare this instance to.</param>
+        /// <returns>True if the other Vector4 is equal to this instance; False otherwise.</returns>
+        [JitIntrinsic]
+        public bool Equals(Vector4 other)
+        {
+            return this.X == other.X
+                && this.Y == other.Y
+                && this.Z == other.Z
+                && this.W == other.W;
+        }
+        #endregion Public Instance Methods
+
+        #region Public Static Methods
+        /// <summary>
+        /// Returns the dot product of two vectors.
+        /// </summary>
+        /// <param name="vector1">The first vector.</param>
+        /// <param name="vector2">The second vector.</param>
+        /// <returns>The dot product.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static float Dot(Vector4 vector1, Vector4 vector2)
+        {
+            return vector1.X * vector2.X +
+                   vector1.Y * vector2.Y +
+                   vector1.Z * vector2.Z +
+                   vector1.W * vector2.W;
+        }
+
+        /// <summary>
+        /// Returns a vector whose elements are the minimum of each of the pairs of elements in the two source vectors.
+        /// </summary>
+        /// <param name="value1">The first source vector.</param>
+        /// <param name="value2">The second source vector.</param>
+        /// <returns>The minimized vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector4 Min(Vector4 value1, Vector4 value2)
+        {
+            return new Vector4(
+                (value1.X < value2.X) ? value1.X : value2.X,
+                (value1.Y < value2.Y) ? value1.Y : value2.Y,
+                (value1.Z < value2.Z) ? value1.Z : value2.Z,
+                (value1.W < value2.W) ? value1.W : value2.W);
+        }
+
+        /// <summary>
+        /// Returns a vector whose elements are the maximum of each of the pairs of elements in the two source vectors.
+        /// </summary>
+        /// <param name="value1">The first source vector.</param>
+        /// <param name="value2">The second source vector.</param>
+        /// <returns>The maximized vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector4 Max(Vector4 value1, Vector4 value2)
+        {
+            return new Vector4(
+                (value1.X > value2.X) ? value1.X : value2.X,
+                (value1.Y > value2.Y) ? value1.Y : value2.Y,
+                (value1.Z > value2.Z) ? value1.Z : value2.Z,
+                (value1.W > value2.W) ? value1.W : value2.W);
+        }
+
+        /// <summary>
+        /// Returns a vector whose elements are the absolute values of each of the source vector's elements.
+        /// </summary>
+        /// <param name="value">The source vector.</param>
+        /// <returns>The absolute value vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector4 Abs(Vector4 value)
+        {
+            return new Vector4(Math.Abs(value.X), Math.Abs(value.Y), Math.Abs(value.Z), Math.Abs(value.W));
+        }
+
+        /// <summary>
+        /// Returns a vector whose elements are the square root of each of the source vector's elements.
+        /// </summary>
+        /// <param name="value">The source vector.</param>
+        /// <returns>The square root vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector4 SquareRoot(Vector4 value)
+        {
+            return new Vector4((Single)Math.Sqrt(value.X), (Single)Math.Sqrt(value.Y), (Single)Math.Sqrt(value.Z), (Single)Math.Sqrt(value.W));
+        }
+        #endregion Public Static Methods
+
+        #region Public static operators
+        /// <summary>
+        /// Adds two vectors together.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The summed vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector4 operator +(Vector4 left, Vector4 right)
+        {
+            return new Vector4(left.X + right.X, left.Y + right.Y, left.Z + right.Z, left.W + right.W);
+        }
+
+        /// <summary>
+        /// Subtracts the second vector from the first.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The difference vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector4 operator -(Vector4 left, Vector4 right)
+        {
+            return new Vector4(left.X - right.X, left.Y - right.Y, left.Z - right.Z, left.W - right.W);
+        }
+
+        /// <summary>
+        /// Multiplies two vectors together.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The product vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector4 operator *(Vector4 left, Vector4 right)
+        {
+            return new Vector4(left.X * right.X, left.Y * right.Y, left.Z * right.Z, left.W * right.W);
+        }
+
+        /// <summary>
+        /// Multiplies a vector by the given scalar.
+        /// </summary>
+        /// <param name="left">The source vector.</param>
+        /// <param name="right">The scalar value.</param>
+        /// <returns>The scaled vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector4 operator *(Vector4 left, Single right)
+        {
+            return left * new Vector4(right);
+        }
+
+        /// <summary>
+        /// Multiplies a vector by the given scalar.
+        /// </summary>
+        /// <param name="left">The scalar value.</param>
+        /// <param name="right">The source vector.</param>
+        /// <returns>The scaled vector.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector4 operator *(Single left, Vector4 right)
+        {
+            return new Vector4(left) * right;
+        }
+
+        /// <summary>
+        /// Divides the first vector by the second.
+        /// </summary>
+        /// <param name="left">The first source vector.</param>
+        /// <param name="right">The second source vector.</param>
+        /// <returns>The vector resulting from the division.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector4 operator /(Vector4 left, Vector4 right)
+        {
+            return new Vector4(left.X / right.X, left.Y / right.Y, left.Z / right.Z, left.W / right.W);
+        }
+
+        /// <summary>
+        /// Divides the vector by the given scalar.
+        /// </summary>
+        /// <param name="value1">The source vector.</param>
+        /// <param name="value2">The scalar value.</param>
+        /// <returns>The result of the division.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector4 operator /(Vector4 value1, float value2)
+        {
+            float invDiv = 1.0f / value2;
+
+            return new Vector4(
+                value1.X * invDiv,
+                value1.Y * invDiv,
+                value1.Z * invDiv,
+                value1.W * invDiv);
+        }
+
+        /// <summary>
+        /// Negates a given vector.
+        /// </summary>
+        /// <param name="value">The source vector.</param>
+        /// <returns>The negated vector.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Vector4 operator -(Vector4 value)
+        {
+            return Zero - value;
+        }
+
+        /// <summary>
+        /// Returns a boolean indicating whether the two given vectors are equal.
+        /// </summary>
+        /// <param name="left">The first vector to compare.</param>
+        /// <param name="right">The second vector to compare.</param>
+        /// <returns>True if the vectors are equal; False otherwise.</returns>
+        [JitIntrinsic]
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static bool operator ==(Vector4 left, Vector4 right)
+        {
+            return left.Equals(right);
+        }
+
+        /// <summary>
+        /// Returns a boolean indicating whether the two given vectors are not equal.
+        /// </summary>
+        /// <param name="left">The first vector to compare.</param>
+        /// <param name="right">The second vector to compare.</param>
+        /// <returns>True if the vectors are not equal; False if they are equal.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static bool operator !=(Vector4 left, Vector4 right)
+        {
+            return !(left == right);
+        }
+        #endregion Public static operators
+    }
+}

mcs/class/referencesource/System.Numerics/System/Numerics/Vector_Operations.cs

@@ -0,0 +1,29 @@
+// Copyright (c) Microsoft. All rights reserved.
+// Licensed under the MIT license. See LICENSE file in the project root for full license information.
+
+using System.Runtime.CompilerServices;
+
+namespace System.Numerics
+{
+    /// <summary>
+    /// Contains various methods useful for creating, manipulating, combining, and converting generic vectors with one another.
+    /// </summary>
+    internal static class Vector
+    {
+        // Every operation must either be a JIT intrinsic or implemented over a JIT intrinsic
+        // as a thin wrapper
+        // Operations implemented over a JIT intrinsic should be inlined
+        // Methods that do not have a <T> type parameter are recognized as intrinsics
+        /// <summary>
+        /// Returns whether or not vector operations are subject to hardware acceleration through JIT intrinsic support.
+        /// </summary>
+        [JitIntrinsic]
+        public static bool IsHardwareAccelerated
+        {
+            get
+            {
+                return false;
+            }
+        }
+    }
+}